Abstract
Typical black hole microstates in AdS/CFT were recently conjectured to have a geometrical dual with a smooth horizon and a portion of a second asymptotic region. I consider the application of the holographic complexity conjectures to this geometry. The holographic calculation leads to divergent values for the complexity; I argue that this classical divergence is consistent with expectations for typical microstates.
Highlights
The AdS=CFT correspondence provides a nonperturbative definition of quantum gravity on asymptotically anti-de Sitter spaces, including black holes in the bulk spacetime
An essential element in the holographic dictionary is understanding the description of black holes in this correspondence, the region behind the horizon. This is understood for the eternal black hole, which is dual to the thermofield double state, a particular entangled state in two copies of the CFT [1]
The aim of the present paper is to test this proposal by considering the application of the holographic complexity conjectures to the geometry in Fig. 1, and comparing to the expectations for the complexity of a typical state
Summary
Typical black hole microstates in AdS=CFT were recently conjectured to have a geometrical dual with a smooth horizon and a portion of a second asymptotic region. I consider the application of the holographic complexity conjectures to this geometry. The holographic calculation leads to divergent values for the complexity; I argue that this classical divergence is consistent with expectations for typical microstates
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